Vijay and Manohar share profits and losses in the ratio of $2:1$. They admit Prakash as a partner with $\frac{1}{4}$ share in profits with a guarantee that his share of profit will be at least $\text{Rs. }50,000$. The net profit of the firm for the year ending March 31, 2015, was $\text{Rs. }1,60,000$. Calculate the amount of profit Vijay will get.

Let's first calculate Prakash's share of the net profit:
$$\text{Prakash’s share}=1,60,000\times \frac{1}{4}=\text{Rs. }40,000$$
Since Prakash was guaranteed a minimum profit of $\text{Rs. }50,000$, there is a deficiency:
$$\text{Deficiency}=50,000-40,000=\text{Rs. }10,000$$
The remaining profit after Prakash's basic share is:
$$\text{Remaining Profit}=1,60,000-40,000=\text{Rs. }1,20,000$$
This remaining profit is divided between Vijay and Manohar in their ratio $2:1$:
$$\text{Vijay’s basic share}=1,20,000\times \frac{2}{3}=\text{Rs. }80,000$$
$$\text{Manohar’s basic share}=1,20,000\times \frac{1}{3}=\text{Rs. }40,000$$
Unless specified otherwise, the deficiency of the guaranteed partner is borne by the old partners in their profit-sharing ratio ($2:1$):
$$\text{Deficiency met by Vijay}=10,000\times \frac{2}{3}=\text{Rs. }6,667$$
$$\text{Vijay’s Final Profit Share}=80,000-6,667=\text{Rs. }73,333$$